If `A` lies in second quadrant and `3tanA+4=0,` then the value of `2cotA-5cos A+sinA` is equal to

Options

A. `-53//10`
B. `23//10`
C. `37//10`
D. `7//10`

Answer

B

Explanation

Here, `3tanA+4 = 0`

`=> tan A = -4/3.`

Now, `cot A = 1/tanA = -3/4`

As , `A` lies in second quadrant,

so, `sinA and cosecA` will be positive and other trigonometric functions will be negative.

Now, `tan A = -4/3`

`:. sec A = sqrt(1+(-4/3)^2) = -5/3`

`:. cosA = -3/5`

...